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Adiabatic control in circuit quantum electrodynamics

Antti P. Vepsäläinen

Published Jan 1, 2018• 0 citations
OpenAlex

Abstract

In circuit quantum electrodynamics the coherence of Cooper pairs in superconductors is employed to create macroscopic electric circuits with quantized energy levels. Such circuits can be coupled with each other and exploited as building blocks of a quantum computer. Accurate and robust control of the quantum state in the circuits is a central condition for the operation of the quantum computer and one of the prerequisites for the implementation of complex algorithms used in quantum information processing, such as quantum error correction. In this thesis adiabatic control in circuit quantum electrodynamics is investigated with the focus on manipulating three-level systems. \n \nIn adiabatic control the eigenstates of the system are slowly modified by changing the external control parameters, which govern the evolution of the system. If the changes in the parameters are slow enough, the state of the system follows the eigenstates in the adiabatic basis, thereby realizing the intended operation. The advantage of adiabatic control is its inherent robustness to small errors or noise in the control parameters; the result of the state manipulation only depends on the asymptotic values of the control parameters, but not on their exact values during the process. \n \nShortcuts to adiabaticity can be used to speed up the otherwise slow adiabatic control by introducing a correction pulse that compensates the diabatic losses during the state manipulation. This allows one to overcome the limitation on the speed of the protocol but simultaneously reduces the method's robustness to the variations in the control parameters. If the level of noise in the control parameters is known, using the shortcut it is possible to find the optimal level of robustness which is required to mitigate the noise. \n \nCircuit quantum electrodynamics offers a perfect experimental platform for investigating quantum control due to the possibility of realizing complicated control schemes using microwave electronics. With commercially available digital-to-analog converters the control signals can be digitally created, which enables accurate and coherent control of the quantum circuit. \n \nIn this thesis both theoretical and experimental results on adiabatic control applied to superconducting transmon circuits are presented. It is shown that stimulated Raman adiabatic passage can be used for population transfer in a three-level transmon, which can be further improved using shortcuts to adiabaticity. Furthermore, a scheme for implementing robust superadiabatic rotation gates in transmon is proposed. Finally, it is demonstrated that superconducting qubit can be used as an ultra-sensitive detector of magnetic flux.

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In circuit quantum electrodynamics the coherence of Cooper pairs in superconductors is employed to create macroscopic electric circuits with quantized energy levels. Such circuits can be coupled with each other and exploited as building blocks of a quantum computer. Accurate and robust control of the quantum state in the circuits is a central condition for the operation of the quantum computer and one of the prerequisites for the implementation of complex algorithms used in quantum information processing, such as quantum error correction. In this thesis adiabatic control in circuit quantum electrodynamics is investigated with the focus on manipulating three-level systems. \n \nIn adiabatic control the eigenstates of the system are slowly modified by changing the external control parameters, which govern the evolution of the system. If the changes in the parameters are slow enough, the state of the system follows the eigenstates in the adiabatic basis, thereby realizing the intended operation. The advantage of adiabatic control is its inherent robustness to small errors or noise in the control parameters; the result of the state manipulation only depends on the asymptotic values of the control parameters, but not on their exact values during the process. \n \nShortcuts to adiabaticity can be used to speed up the otherwise slow adiabatic control by introducing a correction pulse that compensates the diabatic losses during the state manipulation. This allows one to overcome the limitation on the speed of the protocol but simultaneously reduces the method's robustness to the variations in the control parameters. If the level of noise in the control parameters is known, using the shortcut it is possible to find the optimal level of robustness which is required to mitigate the noise. \n \nCircuit quantum electrodynamics offers a perfect experimental platform for investigating quantum control due to the possibility of realizing complicated control schemes using microwave electronics. With commercially available digital-to-analog converters the control signals can be digitally created, which enables accurate and coherent control of the quantum circuit. \n \nIn this thesis both theoretical and experimental results on adiabatic control applied to superconducting transmon circuits are presented. It is shown that stimulated Raman adiabatic passage can be used for population transfer in a three-level transmon, which can be further improved using shortcuts to adiabaticity. Furthermore, a scheme for implementing robust superadiabatic rotation gates in transmon is proposed. Finally, it is demonstrated that superconducting qubit can be used as an ultra-sensitive detector of magnetic flux.
The challenge to fully grasp and to harness the bizarre phenomena which take place in the quantum realm is crucially linked to the ability to engineer and manipulate quantum systems with high precision. The scientific progress in this direction is opening new routes for the investigation of fundamental quantum physics, and it is at the same time paving the way to the development of the first quantum technologies. \n\nThis thesis is dedicated to the search of strategies for high-fidelity and noise-tolerant quantum control.\nA versatile theoretical framework is set up for the design of optimized control protocols based on accelerated adiabatic processes. The benefits of the adiabatic dynamics, rooted in its intrinsic stability versus control imperfections, are released from the requirement of slow evolution: this is achieved thanks to the theoretical construction of accelerating control Hamiltonians which dynamically counteract deviations from the target dynamics. Our framework provides a methodical way to engineer these Hamiltonians by introducing fast modulations of the initially-available control parameters, and it results from the interplay between the theory of counterdiabatic fields and Floquet-Magnus average Hamiltonian theory. As compared to other shortcut-to-adiabaticity strategies, our control method keeps the system always close to the exact adiabatic path while not requiring the implementation of new Hamiltonian couplings. Moreover, the flexibility in the construction of the accelerating Hamiltonians offers a fertile ground for the hybridization with optimal control techniques.\n\nThe general setup is applied to exemplary control problems of relevance in quantum optics and quantum information processing. First, a protocol is designed for the generation of entanglement between effective two-level systems coupled through a transmission line, in the experimental context of circuit quantum electrodynamics. Second, an accelerated version of the widespread technique of stimulated Raman adiabatic passage is presented, which dramatically enlarges its range of applicability for implementations both in the optical and in the microwave regime.\n\nThe results strongly support the potential of the quantum control framework developed in this thesis. In particular, our methodology offers the opportunity to flank high fidelities and small error sensitivity with on-demand adaptability to experimental constraints and the flexibility for integrations with other control techniques. This makes it a valuable resource for applications in many branches of quantum science, with a natural outlet in quantum computation and simulation.
Adiabatic manipulation of the quantum state is an essential tool in modern quantum information processing. Here, we demonstrate the speedup of the adiabatic population transfer in a three-level superconducting transmon circuit by suppressing the spurious nonadiabatic excitations with an additional two-photon microwave pulse. We apply this superadiabatic method to the stimulated Raman adiabatic passage, realizing fast and robust population transfer from the ground state to the second excited state of the quantum circuit.
The adiabatic manipulation of quantum states is a powerful technique that opened up new directions in quantum engineering--enabling tests of fundamental concepts such as geometrical phases and topological transitions, and holding the promise of alternative models of quantum computation. Here we benchmark the stimulated Raman adiabatic passage for circuit quantum electrodynamics by employing the first three levels of a transmon qubit. In this ladder configuration, we demonstrate a population transfer efficiency >80% between the ground state and the second excited state using two adiabatic Gaussian-shaped control microwave pulses. By doing quantum tomography at successive moments during the Raman pulses, we investigate the transfer of the population in time domain. Furthermore, we show that this protocol can be reversed by applying a third adiabatic pulse, we study a hybrid nondiabatic-adiabatic sequence, and we present experimental results for a quasi-degenerate intermediate level.
Shortcuts to adiabaticity are powerful quantum control methods, allowing quick evolution into target states of otherwise slow adiabatic dynamics. Such methods have widespread applications in quantum technologies, and various shortcuts to adiabaticity protocols have been demonstrated in closed systems. However, realizing shortcuts to adiabaticity for open quantum systems has presented a challenge due to the complex controls in existing proposals. Here, we present the experimental demonstration of shortcuts to adiabaticity for open quantum systems, using a superconducting circuit quantum electrodynamics system. By applying a counterdiabatic driving pulse, we reduce the adiabatic evolution time of a single lossy mode from 800 ns to 100 ns. In addition, we propose and implement an optimal control protocol to achieve fast and qubit-unconditional equilibrium of multiple lossy modes. Our results pave the way for precise time-domain control of open quantum systems and have potential applications in designing fast open-system protocols of physical and interdisciplinary interest, such as accelerating bioengineering and chemical reaction dynamics.
The field of quantum computation and simulation has its origins in the early 1980s, when the limitations of the existing paradigm of classical computing machines became apparent. The continuous miniaturization of circuit elements and the increase in their number per unit area will ultimately lead to practical difficulties and to the manifestation of quantum phenomena. This foresight triggered the research work for the invention of new principles of computation. The physical laws of our world are fundamentally quantum mechanical; that is why quantum systems have started to be considered as platforms for possible more powerful computing systems and simulators. Superconducting quantum circuits offer one of the most convenient and promising architectures in this field of research. They are macroscopic and, as a result, provide a better controllability. At the same time they can be produced with customary electronics fabrication methods and they are easily integrable with nowadays electronics. This dissertation contains experimental studies of fully coplanar superconducting quantum circuits comprising a transmon type artificial atom coupled to a quarter-wavelength waveguide resonator. This circuit represents the simplest simulator of light-matter interaction and acts as a testbed for the gate operations needed to control the quantum state in the field of quantum computation. The stimulated Raman adiabatic passage and the shortcut to its adiabaticity were experimentally studied as methods for the efficient population transfer between the ground and the second excited state of the transmon. The possibility of using a hybrid adiabatic-nonadiabatic pulse sequences for preparing an arbitrary quantum three-level state was shown theoretically. The operation of gates based on geometric phases was implemented on the same type of superconducting structure. Finally, the structure was used as a magnetic flux sensor. The magnetic flux resolution of this sensor is enhanced by the use of two properly modified phase estimation algorithms and it is potentially limited only by the Heisenberg uncertainty principle. The superiority of the realized sensor over the standard classical measurement done on the same sample is clearly demonstrated. This experiment indicates the utility of superconducting quantum circuits for the tasks of quantum metrology.
Construction of optimal gate operations is significant for quantum computation. Here an efficient scheme is proposed for performing shortcut-based quantum gates on superconducting qubits in circuit quantum electrodynamics (QED). Two four-level artificial atoms of Cooper-pair box circuits, having sufficient level anharmonicity, are placed in a common quantized field of circuit QED and are driven by individual classical microwaves. Without the effect of cross resonance, one-qubit NOT gate and phase gate in a decoupled atom can be implemented using the invariant-based shortcuts to adiabaticity. With the assistance of cavity bus, a one-step SWAP gate can be obtained within a composite qubit-photon-qubit system by inversely engineering the classical drivings. We further consider the gate realizations by adjusting the microwave fields. With the accessible decoherence rates, the shortcut-based gates have high fidelities. The present strategy could offer a promising route towards fast and robust quantum computation with superconducting circuits experimentally.